This dissertation explores the capability of dense seismic array data for imaging the rupture properties of earthquake sources using a method known as back-projection. Only within the past 10 or 15 years has implementation of the method become feasible through the development of large aperture seismic arrays such as the High Sensitivity Seismograph Network in Japan and the Transportable Array in the United States. Coincidentally, this buildup in data coverage has also been accompanied by a global cluster of giant earthquakes (Mw>8.0). Much of the material in this thesis is devoted to imaging the source complexity of these large events. In particular, evidence for rupture segmentation, dynamic triggering, and frequency dependent energy release is presented. These observations have substantial implications for evaluating the seismic and tsunami hazards of future large earthquakes. In many cases, the details of the large ruptures can only be imaged by the back-projection method through the addition of different data sets and incorporating additional processing steps that enhance low-amplitude signals. These improvements to resolution can also be utilized to study much smaller events. This approach is taken for studying two very different types of earthquakes. First, a global study of the enigmatic intermediate-depth (100-300 km) earthquakes is performed. The results show that these events commonly have sub-horizontal rupture planes and suggest dynamic triggering of multiple sub-events. From these observations, a hypothesis for the generation of intermediate-depth events is proposed. Second, the early aftershock sequences of the 2004 Mw 9.1 Sumatra-Andaman and 2011 Mw 9.0 Tohoku, Japan earthquakes are studied using the back-projection method. These analyses show that many events can be detected that are not in any local or global earthquake catalogues. In particular, the locations of aftershocks in the back-projection results of the 2011 Tohoku sequence fill in gaps in the aftershock distribution of the Japan Meteorological Agency catalogue. These results may change inferences of the behavior of the 2011 mainshock, as well as the nature of future seismicity in this region. In addition, the rupture areas of the largest aftershocks can be determined, and compared to the rupture area of the mainshock. For the Tohoku event, this comparison reveals that the aftershocks contribute significantly to the cumulative failure area of the subduction interface. This result implies that future megathrust events in this region can have larger magnitudes than the 2011 event.